What is the integral of (5x^{-3}-2) ?

The integral of (5x^{-3}-2) is -5/(2x^2)-2x+C

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integral of (5x^{-3}-2)

\int (5 x^{- 3} - 2) d x

- \frac{5}{2 x ^{2}} - 2 x + C

Solution steps

\int 5 x^{- 3} - 2 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5 x^{- 3} d x - \int 2 d x

\int 5 x^{- 3} d x = - \frac{5}{2 x ^{2}}

\int 2 d x = 2 x

= - \frac{5}{2 x ^{2}} - 2 x

Add a constant to the solution

= - \frac{5}{2 x ^{2}} - 2 x + C

What is the integral of (5x^{-3}-2) ?
The integral of (5x^{-3}-2) is -5/(2x^2)-2x+C